Relativity 1

Relativity 1#

Example 2: The Moving Sidewalk, er…train#

The Question: Look at this picture of a train moving by we observers, who are on the ground.

galilean_train

The lady on the train is in a row that measures \(d_A\) feet from the left edge of the car.

  • \(d_A\) = 50 feet

The train is traveling at \(u=20.5\) mph, which is about \(u=30\) ft/s relative to the ground.

  • \(u=30\) ft/s

Notice that we’re looking at this situation from the ground since the train is already labeled as the Away frame and the ground, the Home frame. So the distance from the origin of the Home frame to the passenger on the moving train is:

  • \(d_H\) which changes with time, right?

  • \(d_H\) is what we want to know after some passage of time from when the two origins overlapped as the train goes by

That time is: \(\Delta t = 30\) s.

What is \(d_H\)?

The Answer:

\[\begin{split} \begin{align*} d_H &= d_A + d_H \text{ which you can see by just looking at the arrows} \\ d_H &= d_A + u\Delta t \\ d_H &= 50 \text{ ft}+ 30 \text{ ft/s}\times 30 \text{ s} \\ d_H &= 50 + 900 = 950 \text{ ft} \end{align*} \end{split}\]
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